Brianna's teacher asks her which of these three expressions are equivalent to each other.

expression a: 9x-3x-4
expression b: 12x-4
expression c: 5x+x-4

brianna says that all three expressions are equivalent because the value of each one is -4 when x=0.

brianna's thinking is incorrect.

• identify the error in brianna's thinking.
• determine which of the three expressions are equivalent.
• explain or show your process in determining which expressions are equivalent.

1. Brianna's thinking is incorrect because of course, when x is 0, the expression will equal whatever value isn't an x term. To find equivalent expression, you actually need to find which expressions have the same amount of x terms and the same value.

2. Expressions A and C are equivalent.

3. Expression A can be simplified, as you can do 9x - 3x = 6x, so your final expression would be 6x - 4. Expression C can also be simplified with 5x + x = 6x, which can then also be written as 6x - 4. This means both expressions have the same amount of x terms, and the same value, so they are equivalent.

I hope this helps!